Dynamic Programming: Knapsack - 0/1 Knapsack Problem
What is the time complexity of the standard bottom-up dynamic programming solution for the 0/1 Knapsack problem with n items and capacity W?
What is the time complexity of the standard bottom-up dynamic programming solution for the 0/1 Knapsack problem with n items and capacity W?
medium🧠 Conceptual Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand DP table size
The DP table has dimensions n (items) by W (capacity).Step 2: Analyze nested loops
Each item iteration loops through capacities 0 to W, resulting in O(n * W) operations.Final Answer:
Option C -> Option CQuick Check:
DP table size matches time complexity [OK]
Quick Trick: Bottom-up 0/1 Knapsack runs in O(n*W) time [OK]
Common Mistakes:
MISTAKES- Assuming linear time ignoring capacity dimension
- Confusing with exponential brute force
- Mistaking quadratic complexity in n only
Trap Explanation:
PITFALL- Ignoring capacity dimension leads to underestimating complexity; exponential is brute force.
Interviewer Note:
CONTEXT- Tests understanding of DP time complexity for 0/1 Knapsack.
Master "0/1 Knapsack Problem" in Dynamic Programming: Knapsack
Want More Practice?
15+ quiz questions · All difficulty levels · Free
Free Signup - Practice All QuestionsMore Dynamic Programming: Knapsack Quizzes